Question about wave interference and coherence

In summary, superposition of waves is when two or more waves from coherent sources meet and superpose to form a resultant wave such that the amplitude of the resultant wave at any point is the vector sum of the amplitudes of the constituent waves at that point.If the amplitude of the resultant wave is greater than the amplitude of one constituent wave but less than the amplitude of another constituent wave, is the interference constructive or destructive?Interference is a wave phenomenon in which two or more waves from coherent sources meet and superpose to form a resultant wave such that the amplitude of the resultant wave at any point is the vector sum of the amplitudes of the constituent waves at that point. destructive interference occurs when the amplitude of the resultant wave
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Fionn Munnelly
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I have encountered the following definition of interference:

Interference is a wave phenomenon in which two or more waves from coherent sources meet and superpose to form a resultant wave such that the amplitude of the resultant wave at any point is the vector sum of the amplitudes of the constituent waves at that point.

If constructive interference occurs, then the amplitude of the resultant wave is greater than the amplitude of anyone of the constituent waves.

If destructive interference occurs, then the amplitude of the resultant wave is less than the amplitude of anyone of the constituent waves.

If the amplitude of the resultant wave is greater than the amplitude of one constituent wave but less than the amplitude of another constituent wave, is the interference constructive or destructive?

In addition, why must the sources of the waves be coherent? Is this only so that any interference pattern produced is stable and unchanging with time? Is the superposition of waves from non-coherent sources to form a resultant wave not still, technically, interference?
 
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  • #2
Fionn Munnelly said:
Is the superposition of waves from non-coherent sources to form a resultant wave not still, technically, interference?
There will be a resultant of phasor addition of the two sources at all points in space. If the sources are of slightly different but constant frequencies then, at all points, this resultant will constantly vary in amplitude and phase. If you take a snapshot of the pattern at anyone time, you will see an interference pattern. This pattern will be for ever changing - marching over the field at the rate determined by the frequency difference and the speed of the wave.

If you insisted, I could possibly agree that there will be a pattern for any pair of waves but it wouldn't be easy to detect and it becomes a bit of a nonsense. Consequently, we reserve the term Interference Pattern for situations when the two sources are either precisely the same frequency or when their frequencies are near enough to identify an interference pattern which 'crawls' very slowly.

The other point about coherence is that every source has phase noise and that gives a finite length over which the phases of two sources maintain the same relationship any point. This gives rise to the idea of coherence length which, as a practicality, limits the width of the optical two slits pattern because of the significantly different path lengths from the two slits relative to this coherence length. The fringes at the edges get fuzzier and fuzzier.
 
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  • #3
Fionn Munnelly said:
If the amplitude of the resultant wave is greater than the amplitude of one constituent wave but less than the amplitude of another constituent wave, is the interference constructive or destructive?
This is where the English language descriptions get a bit fuzzy so you should just stick to the math. Nature doesn't really care what we call it. Perhaps an English language term that would satisfy you as being more consistently in line with the math over the full range would be simply "interaction" between the waves.
 
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  • #4
phinds said:
simply "interaction" between the waves
Yes. You pretty much fully described the situation when you said
"the resultant wave at any point is the vector sum of the amplitudes of the constituent waves at that point."
Sometimes when you add vectors they get bigger, sometimes smaller, that is all.
 
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  • #5
@phinds and @DaveE This is yet another result of 'teaching by numbers'. Students are taught in terms of categories rather than how to understand what's actually going on. They are (or at least they feel they are) assessed in terms of sound bytes. The result is confusion when in the real world.
 
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phinds said:
Perhaps an English language term that would satisfy you as being more consistently in line with the math over the full range would be simply "interaction" between the waves.
DaveE said:
Yes. You pretty much fully described the situation when you said
"the resultant wave at any point is the vector sum of the amplitudes of the constituent waves at that point."
Sometimes when you add vectors they get bigger, sometimes smaller, that is all.
Among physicists, the commonly used term for this is "superposition" of waves.
 
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  • #7
Fionn Munnelly said:
If the amplitude of the resultant wave is greater than the amplitude of one constituent wave but less than the amplitude of another constituent wave, is the interference constructive or destructive?

It's neither.
 
  • #8
sophiecentaur said:
Students are taught in terms of categories rather than how to understand what's actually going on.

I'm sure that that happens quite often. But even if the teacher emphasizes sense-making, many students will still revert to that answer-making strategy as their go-to learning scheme.
 
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  • #9
Mister T said:
students will still revert to that answer-making strategy
Especially when so many questions are multiple choice.
 
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Related to Question about wave interference and coherence

1. What is wave interference?

Wave interference is the phenomenon that occurs when two or more waves meet and overlap in the same medium. This results in the combination of the waves, causing them to either amplify or cancel each other out depending on their amplitudes and phases.

2. How does wave interference affect the behavior of waves?

Wave interference can cause changes in the amplitude, frequency, and direction of waves. When waves interfere constructively, their amplitudes add together and create a larger amplitude wave. When waves interfere destructively, their amplitudes cancel each other out and create a smaller amplitude wave.

3. What is the difference between constructive and destructive interference?

Constructive interference occurs when two waves meet and have the same frequency and phase, resulting in an increase in amplitude. Destructive interference occurs when two waves meet and have opposite phases, resulting in a decrease in amplitude.

4. How does coherence affect wave interference?

Coherence is the measure of how well two waves maintain a constant phase relationship. When two waves are coherent, they have a consistent phase difference and can interfere constructively or destructively. If the waves are not coherent, they will not interfere with each other.

5. What are some real-life examples of wave interference and coherence?

Some examples of wave interference and coherence in everyday life include the colors seen in soap bubbles, the sound produced by two musical instruments playing the same note, and the patterns formed by overlapping ripples in a pond. In technology, coherence is important in fiber optic communication and in the functioning of lasers.

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